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Iterative Methods for Computing Vibrational Spectra

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  • Tucker Carrington

    (Chemistry Department, Queen’s University, Kingston, ON K7L 3N6, Canada)

Abstract

I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate ( F ) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.

Suggested Citation

  • Tucker Carrington, 2018. "Iterative Methods for Computing Vibrational Spectra," Mathematics, MDPI, vol. 6(1), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:1:p:13-:d:127248
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